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We consider a setting in which we have a treatment and a potentially large number of covariates for a set of observations, and wish to model their relationship with an outcome of interest. We propose a simple method for modeling interactions between the treatment and covariates. The idea is to modify the covariate in a simple way, and then fit a standard model using the modified covariates and no main effects. We show that coupled with an efficiency augmentation procedure, this method produces clinically meaningful estimators in a variety of settings. It can be useful for practicing personalized medicine: determining from a large set of biomarkers, the subset of patients that can potentially benefit from a treatment. We apply the method to both simulated datasets and real trial data. The modified covariates idea can be used for other purposes, for example, large scale hypothesis testing for determining which of a set of covariates interact with a treatment variable. Supplementary materials for this article are available online.

This paper explores a methodology for dimension reduction in regression models for a treatment outcome, specifically to capture covariates’ moderating impact on the treatment-outcome association. The motivation behind this stems from the field of precision medicine, where a comprehensive understanding of the interactions between a treatment variable and pretreatment covariates is essential for developing individualized treatment regimes (ITRs). We provide a review of sufficient dimension reduction methods suitable for capturing treatment-covariate interactions and establish connections with linear model-based approaches for the proposed model. Within the framework of single-index regression models, we introduce a sparse estimation method for a dimension reduction vector to tackle the challenges posed by high-dimensional covariate data. Our methods offer insights into dimension reduction techniques specifically for interaction analysis, by providing a semiparametric framework for approximating the minimally sufficient subspace for interactions.

The Papadakis covariate is commonly used to account for spatial variation in agricultural field experiments. However, it is calculated from the observed yield, and is affected by unexpected land discontinuity. To address this problem, we propose two extensions. First, we introduce a kriged residual and the kriged Papadakis residual, are discussed. The second extension is a modification of the conventional Papadakis covariate that assigns equal weight to neighboring plots, regardless of their distance from the point of interest. The proposed covariate (a modified Papadakis covariate) assigns different weights to plot yield according to their spatial position. The proposed extensions are compared to the conventional Papadakis covariate using field data from Ethiopia. Simulations were conducted to evaluate the performance of these covariates. The number of neighbors needed to compute the proposed covariate are determined by the range of the variogram.

The paper describes a complex multistate modelling approach for the analysis of association between the onset of diabetes and the diagnosis of pancreatic cancer among families with hereditary pancreatitis. The model allows for competing risks, correlated survival times and time-dependent covariates, so taking several interrelated factors into account: the consequences of pancreatic resection, genetic similarities between family members and the possibility that the onset of diabetes is the first symptom of an undiagnosed pancreatic cancer. The model is applied to data on diabetes and cancer outcomes for 593 pancreatitis patients, taken from the world's largest registry of patients with heredity pancreatitis.

Cigarette smoking is a prototypical example of a recurrent event. The pattern of recurrent smoking events may depend on time-varying covariates including mood and environmental variables. Fixed effects and frailty models for recurrent events data assume that smokers have a common association with time-varying covariates. We develop a mixed effects version of a recurrent events model that may be used to describe variation among smokers in how they respond to those covariates, potentially leading to the development of individual-based smoking cessation therapies. Our method extends the modified EM algorithm of Steele (1996) for generalized mixed models to recurrent events data with partially observed time-varying covariates. It is offered as an alternative to the method of Rizopoulos, Verbeke, and Lesaffre (2009) who extended Steele's (1996) algorithm to a joint-model for the recurrent events data and time-varying covariates. Our approach does not require a model for the time-varying covariates, but instead assumes that the time-varying covariates are sampled according to a Poisson point process with known intensity. Our methods are well suited to data collected using Ecological Momentary Assessment (EMA), a method of data collection widely used in the behavioral sciences to collect data on emotional state and recurrent events in the every-day environments of study subjects using electronic devices such as Personal Digital Assistants (PDA) or smart phones.

Discrete-time discrete-state Markov chain models can be used to describe individual change in categorical variables. But when the observed states are subject to measurement error, the observed transitions between two points in time will be partially spurious. Latent Markov models make it possible to separate true change from measurement error The standard latent Markov model is, however, rather limited when the aim is to explain individual differences in the probability of occupying a particular state at a particular point in time. This paper presents a flexible logit regression approach which allows to regress the latent states occupied at the various points in time on both time- constant and time-varying covariates. The regression approach combines features of causal log-linear models and latent class models with explanatory variables. In an application pupils' interest in physics at different points in time is explained by the time-constant covariate sex and the time-varying covariate physics grade. Results of both the complete and partially observed data are presented.